Restrictions on realizable unitary operations imposed by symmetry and locality
Restrictions on realizable unitary operations imposed by symmetry and locality
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DOI：
10.1038/s41567-021-01464-0
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发表时间：
2020-03
期刊：
影响因子：
19.6
通讯作者：
I. Marvian
中科院分区：
文献类型：
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作者：
I. Marvian
根据量子计算中的一个基本结果，复合系统上的任何幺正变换都可以使用所谓的2-局部幺正来生成，这些幺正只作用于两个子系统。除了在量子计算中的重要性之外，这个结果也可以被看作是关于具有局部哈密顿量的系统的动力学的陈述：虽然局部性对短期动力学施加了各种约束，但它并不限制具有一般局部哈密顿量的复合系统在足够长的时间后可能经历的幺正演化。在这里，我们表明，这种普适性并不保持有效的守恒定律和整体连续对称性，如U（1）和SU（2）的存在。特别是，我们表明，通用对称酉不能实现，甚至近似，使用本地对称酉。基于这个不去定理，我们提出了一种方法，实验探测的相互作用在自然界中的局部性。在量子热力学的背景下，我们的研究结果意味着，一般的能量守恒幺正变换的复合系统不能仅仅通过结合当地的能量守恒幺正的组件。我们展示了如何通过催化来规避这一点。
According to a fundamental result in quantum computing, any unitary transformation on a composite system can be generated using so-called 2-local unitaries that act only on two subsystems. Beyond its importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time. Here we show that this universality does not remain valid in the presence of conservation laws and global continuous symmetries such as U(1) and SU(2). In particular, we show that generic symmetric unitaries cannot be implemented, even approximately, using local symmetric unitaries. Based on this no-go theorem, we propose a method for experimentally probing the locality of interactions in nature. In the context of quantum thermodynamics, our results mean that generic energy-conserving unitary transformations on a composite system cannot be realized solely by combining local energy-conserving unitaries on the components. We show how this can be circumvented via catalysis.